Markovic has become Liverpool's fourth close-season signing after joining on a long-term deal, the Premier league club said on Tuesday.
No fee was announced but media reports said the 20-year-old had been signed from Benfica for 20 million pounds (USD 34.03 million).
The highly-rated left-sided attacker joins England internationals and former Southampton pair Rickie Lambert and Adam Lallana as well as Germany Under-21 midfielder Emre Can at Anfield.
"I am very happy that I have joined such a great club," Markovic said on the club website.
"I hope that I will fulfil the expectations of the supporters, coaches, players and all connected to the club. I have seen what the players are like, I have seen what the supporters are like, and I cannot wait to start playing here,” he added.
Belgium striker Divock Origi is also close to joining Liverpool in a 10 million euro deal from Lille, according to media reports, as manager Brendan Rodgers bolsters his squad after the departure of Uruguay forward Luis Suarez to Barcelona.
A former Partizan Belgrade player, Markovic helped Benfica win the Portuguese title last season after joining the club in June 2013.
"This is an exciting signing for us and one that improves our squad, in terms of attacking options, for the coming season," Rodgers said.
"He was hugely impressive for Benfica last season and has proved he has the ability to produce the goods in European competition as well, which will be important for us,” he added.
Meanwhile, Chelsea's new striker Diego Costa, a 32 million pound (USD 54.87 million) signing from Atletico Madrid at the start of the month, has completed his transfer and signed a five-year deal, the London-based club said on Tuesday.
"I am very happy to sign for Chelsea. Everybody knows it is a big club in a very competitive league, and I am very excited to get started in England with a fantastic coach and team mates," Costa, 25, was quoted as saying on the club's website.
"I know the high quality of the squad I am joining,” he added.
"I would like to thank everybody at Atletico who made me into the player I am. It was an incredible time for me, but now I am starting a new adventure and I hope to win many trophies with Chelsea,” he said.
Powerful and direct, the Brazilian-born striker built a strong reputation in Spain as a fine finisher, scoring 64 goals in 134 appearances for Atletico, and helping them to the Spanish title last season and the Champions League final.


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